Introduction to Differential Equations with Dynamical Systems

ISBN-10: 0691124744

ISBN-13: 9780691124742

Edition: 2008

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Description:

Many textbooks on differential equations are written to be interesting to the teacher rather than the student.Introduction to Differential Equations with Dynamical Systemsis different. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length. Professors: A supplementary Solutions Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/solutions.html
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Book details

List price: $125.00
Copyright year: 2008
Publisher: Princeton University Press
Publication date: 4/21/2008
Binding: Hardcover
Pages: 472
Size: 7.25" wide x 10.50" long x 1.00" tall
Weight: 2.618
Language: English

Preface
First-Order Differential Equations and Their Applications
Introduction to Ordinary Differential Equations
The Definite Integral and the Initial Value Problem
The Initial Value Problem and the Indefinite Integral
The Initial Value Problem and the Definite Integral
Mechanics I: Elementary Motion of a Particle with Gravity Only
First-Order Separable Differential Equations
Using Definite Integrals for Separable Differential Equations
Direction Fields
Existence and Uniqueness
Euler's Numerical Method (optional)
First-Order Linear Differential Equations
Form of the General Solution
Solutions of Homogeneous First-Order Linear Differential Equations
Integrating Factors for First-Order Linear Differential Equations
Linear First-Order Differential Equations with Constant Coefficients and Constant Input
Homogeneous Linear Differential Equations with Constant Coefficients
Constant Coefficient Linear Differential Equations with Constant Input
Constant Coefficient Differential Equations with Exponential Input
Constant Coefficient Differential Equations with Discontinuous Input
Growth and Decay Problems
A First Model of Population Growth
Radioactive Decay
Thermal Cooling
Mixture Problems
Mixture Problems with a Fixed Volume
Mixture Problems with Variable Volumes
Electronic Circuits
Mechanics II: Including Air Resistance
Orthogonal Trajectories (optional)
Linear Second- and Higher-Order Differential Equations
General Solution of Second-Order Linear Differential Equations
Initial Value Problem (for Homogeneous Equations)
Reduction of Order
Homogeneous Linear Constant Coefficient Differential Equations (Second Order)
Homogeneous Linear Constant Coefficient Differential Equations (nth-Order)
Mechanical Vibrations I: Formulation and Free Response
Formulation of Equations
Simple Harmonic Motion (No Damping, [delta] = 0)
Free Response with Friction ([delta] > 0)
The Method of Undetermined Coefficients
Mechanical Vibrations II: Forced Response
Friction is Absent ([delta] = 0)
Friction is Present ([delta] > 0) (Damped Forced Oscillations)
Linear Electric Circuits
Euler Equation
Variation of Parameters (Second-Order)
Variation of Parameters (nth-Order)
The Laplace Transform
Definition and Basic Properties
The Shifting Theorem (Multiplying by an Exponential)
Derivative Theorem (Multiplying by t)
Inverse Laplace Transforms (Roots, Quadratics, and Partial Fractions)
Initial Value Problems for Differential Equations
Discontinuous Forcing Functions
Solution of Differential Equations
Periodic Functions
Integrals and the Convolution Theorem
Derivation of the Convolution Theorem (optional)
Impulses and Distributions
An Introduction to Linear Systems of Differential Equations and Their Phase Plane
Introduction
Introduction to Linear Systems of Differential Equations
Solving Linear Systems Using Eigenvalues and Eigenvectors of the Matrix
Solving Linear Systems if the Eigenvalues are Real and Unequal
Finding General Solutions of Linear Systems in the Case of Complex Eigenvalues
Special Systems with Complex Eigenvalues (optional)
General Solution of a Linear System if the Two Real Eigenvalues are Equal (Repeated) Roots
Eigenvalues and Trace and Determinant (optional)
The Phase Plane for Linear Systems of Differential Equations
Introduction to the Phase Plane for Linear Systems of Differential Equations
Phase Plane for Linear Systems of Differential Equations
Real Eigenvalues
Complex Eigenvalues
General Theorems
Mostly Nonlinear First-Order Differential Equations
First-Order Differential Equations
Equilibria and Stability
Equilibrium
Stability
Review of Linearization
Linear Stability Analysis
One-Dimensional Phase Lines
Application to Population Dynamics: The Logistic Equation
Nonlinear Systems of Differential Equations in the Plane
Introduction
Equilibria of Nonlinear Systems, Linear Stability Analysis of Equilibrium, and the Phase Plane
Linear Stability Analysis and the Phase Plane
Nonlinear Systems: Summary, Philosophy, Phase Plane, Direction Field, Nullclines
Population Models
Two Competing Species
Predator-Prey Population Models
Mechanical Systems
Nonlinear Pendulum
Linearized Pendulum
Conservative Systems and the Energy Integral
The Phase Plane and the Potential
Answers to Odd-Numbered Exercises
Index
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